轴向运动曲梁的次谐分岔和混沌
Subharmonic Bifurcations and Chaos for the Buckled Beam at Axial Motion
DOI: 10.12677/AAM.2019.87149, PDF,    科研立项经费支持
作者: 王 晶, 张冬梅：临沂大学数学与统计学院，山东 临沂
关键词: 屈曲梁；次谐分岔；混沌；Melnikov方法；Buckled Beam； Subharmonic Bifurcations； Chaos； Melnikov Methods
摘要: 研究了一类轴向运动屈曲梁的次谐分岔和混沌行为。利用Melnikov方法，给出了屈曲梁异宿轨道Melnikov函数和次谐Melnikov函数的表达式，得到系统出现次谐分岔和超次谐分岔的参数条件，给出系统混沌区域和非混沌区域的分界曲线。根据参数的取值范围做数值模拟，结果验证了理论分析。
Abstract: The subharmonic bifurcations and chaos for one kind of buckled beam model subjected to para-metric excitations are investigated. The critical curves separating the chaotic and non-chaotic re-gions are obtained by utilizing Melnikov method. The conditions for subharmonic bifurcations are also obtained. Numerical results are given, which verify the analytical ones.
文章引用：王晶, 张冬梅. 轴向运动曲梁的次谐分岔和混沌[J]. 应用数学进展, 2019, 8(7): 1277-1283. https://doi.org/10.12677/AAM.2019.87149

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